Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

V. M. Bezpalchuk$^{1}$, R. Kozubski$^{2}$, A. M. Gusak$^{1}$

$^1$Bohdan Khmelnytsky National University of Cherkasy, 81 Shevchenko Blvd., 18031 Cherkasy, Ukraine
$^2$M. Smoluchowski Institute of Physics, Jagiellonian University in Krakow, Lojasiewicza 11, PL-30-348 Krakow, Poland

Received: 02.07.2017. Download: PDF

Tracer diffusion and ‘chemical’ (atomic) ordering processes in two face-centred cubic (f.c.c.) binary systems mimicking Ni$_{3}$Al and FePt were simulated by means of the kinetic mean-field (KMF) method originally proposed by G. Martin in 1990. The systems simulated within the present work were modelled with fixed pair-interaction parameters and saddle-point energies adopted earlier $via$ the comparison of Monte Carlo method modelling and experimental data. In a simulation of tracer migration as well as ordering, the focus was attracted to comparison of activation energies rather than pre-exponential factors of kinetic coefficients. Generally, the mean-field models cannot properly take into account correlation effect that could be important for the tracer diffusion especially for the $B$2 structures. However, at least for the f.c.c. structures, application of KMF to diffusion and ordering seems demonstrating very reasonable results qualitatively similar to those obtained in kinetic Monte Carlo (KMC) method and realistic experiments. Modelling of Ni- and Al-tracer diffusion in Ni$_{3}$Al system shows higher diffusivity of Ni atoms as compared with Al ones that is attributed to easier intrasublattice diffusion channel for the Ni atoms in the $L1_{2}$-Ni$_{3}$Al superstructure. Also, the obtained activation energy for the tracer Al atoms is higher, and its value is closer to activation energy of ordering kinetics. Computer experiments for the ordering kinetics showed that, in contrast to exchange mechanism, $L1_{2}$-type ordering kinetics is described $via$ two relaxation times in case of the vacancy diffusion mechanism. Modelling of the discontinuous process of the surface-induced re-orientation of the monatomic Fe and Pt planes in thin FePt film was, in turn, a good test for the stochastic variant of the KMF (SKMF) method. The fact that implementation of the stochastic noise was needed to reproduce the process of a surface nucleation by KMF indicates the correctness of the method.

Keywords: kinetic mean-field method, tracer diffusion, ordering kinetics, atomistic simulation, intermetallics.

PACS: 02.70.-c, 02.70.Uu, 34.10.+x, 64.60.Cn, 64.60.De,


Citation: V. M. Bezpalchuk, R. Kozubski, and A. M. Gusak, Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method, Usp. Fiz. Met., 18, No. 3: 205—233 (2017), doi: 10.15407/ufm.18.03.205

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